2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147223Let $K$ be a field finitely generated over the field of rational numbers, $K(c)$ the extension of $K$ obtained by adjoining all roots of unity, $L$ an infinite Galois extension of $K$, $X$ an abelian variety defined over $K$. We prove that under certain conditions on $X$ and $K$ the existence of infinitely many L-rational points of finite order on $X$ implies that the intersection of $L$ and $K(c)$ has infinite degree over $K$.LaTeX 2e 17 pagesAlgebraic Geometry14K15 (Primary) 11G10 (Secondary)text